Progress in Wall Turbulence 2

The scaling of size of the momentum-bearing eddies in wall-parallel planes in the outer part of turbulent wall layers is analyzed, by examining spectra of the fluctuating velocities taken from direct numerical simulations and experiments. For all flows under scrutiny the normalized spectra highlight growth of the eddies size with the wall distance. The results indicate the capability of a modified mixing length (Pirozzoli, J Fluid Mech 702:521–532, 2012 [

1

]) of accounting with greater precision for the wall-normal variation of the size of the eddies bearing streamwise momentum. This observation can be explained by assuming that outer layer momentum streaks (superstructures) spread under the collective action of the other eddies, which impart a (nearly) uniform eddy diffusivity throughout the outer wall layer.

A turbulence model designed and calibrated in the steady RANS (Reynolds-Averaged Navier-Stokes) framework has usually been straightforwardly applied to an unsteady calculation. It mostly ended up in a steady velocity field in the case of confined wall-bounded flows; a somewhat better outcome is to be expected in globally unstable flows, such as bluff body configurations. However, only a weakly unsteady mean flow can be returned with the level of unsteadiness being by far lower compared to a referent database. The latter outcome motivated the present work dealing with an appropriate extension of a near-wall Second-Moment Closure (SMC) RANS model towards an instability-sensitive formulation. Accordingly, a Sensitized-RANS (SRANS) model based on a differential, near-wall Reynolds stress model of turbulence, capable of resolving the turbulence fluctuations to an extent corresponding to the model’s self-balancing between resolved and modelled (unresolved) contributions to the turbulence kinetic energy, is formulated and applied to several attached and separated wall-bounded configurations—channel and duct flows, external and internal flows separating from sharp-edged and continuous curved surfaces. In most cases considered the fluctuating velocity field was obtained started from the steady RANS results. The model proposed does not comprise any parameter depending explicitly on the grid spacing. An additional term in the corresponding length scale-determining equation providing a selective assessment of its production, modelled in terms of the von Karman length scale (formulated in terms of the second derivative of the velocity field) in line with the SAS (Scale-Adaptive Simulation) proposal (Menter and Egorov, Flow Turbul Combust 85:113–138, (2010) [

14

]), represents here the key parameter.

The current knowledge about some particular kinds of coherent structures in the logarithmic and outer layers of wall-bounded turbulent flows is briefly reviewed. It is shown that a lot has been learned about their geometry, flow properties and temporal behaviour. It is also shown that, although the wall-attached structures carry the largest fraction of most flow properties, they are only extreme cases of smaller wall-detached eddies, and that the latter connect with the more classical behaviour of homogeneous turbulence away from walls. Nevertheless, it is argued that little is known about the dynamical origin of these structures, and that a concerned effort is required to quantitatively identify which one (or ones) of the plausible available dynamical models is a better representation of the observed behaviour.

The attached eddy hypothesis of Townsend [

16

] is the basis of a model of the logarithmic region in wall-bounded turbulent flows, in which the inertially dominated part of the flow is described by a hierarchy of self-similar eddying motions that extend to the wall. The hypothesis has gained considerable support from high Reynolds number experiments and recently from DNS Sillero et al., Phys. Fluids 25:105102, 2013, [

14

]. Meneveau and Marusic, J. Fluid Mech., 719:R1, 2013, [

9

] also recently used the attached eddy hypothesis, together with the central limit theorem, to deduce that all even-ordered moments of the streamwise velocity will exhibit a logarithmic dependence on the distance from the wall. This was also further supported by experimental evidence.

In this investigation, Direct Numerical Simulations (DNS) of turbulent spatially developing boundary layers (SDBL) with prescribed Very Strong Favorable Pressure Gradients (VSFPG) are performed by means of the Dynamic Multi-scale Approach (DMA) developed by Araya et al. JFM, 670:518–605, 2011 [

1

]. Although the prescription of an external VSFPG significantly reduces turbulence production, the flow never becomes completely laminar due to the finite value of the streamwise Reynolds normal stress, and thus the flow is quasi-laminar. In this sense, the mean flow carries the footprint of turbulence, particularly in the streamwise direction of the Reynolds stresses. In addition, the vertical transports toward the wall of

$$\overline{v'^{2+}}$$

v

′

2

+

¯

and

$$\overline{uv'^{+}}$$

u

v

′

+

¯

practically disappear in the inner region and significantly decrease in the outer region of the boundary layer during the quasi-laminarization stage. As a consequence, the “communication” between inner and outer regions is seriously restricted.

Reproduction of atmospheric boundary layer wind tunnel experiments by numerical simulation is achieved in this work by directly modeling, with immersed boundary method, the geometrical elements placed in the wind tunnel’s floor to induce the desired characteristics to the boundary layer. The numerical model is implemented on the basis of the open-source flow solver caffa3d.MBRi, which uses a finite volume method over block structured grids, coupled with various LES approaches for turbulence modeling and parallelization through domain decomposition with MPI. The Immersed boundary method approach followed the work of Liao et al. (Simulating flows with moving rigid boundary using immersed-boundary method. Comput. Fluids 39, 152–167, 2010). Numerical simulation results are compared to wind tunnel measurements for the mean velocity profiles, rms profiles, and spectrums, providing good overall agreement. We conclude that the Immersed Boundary Condition method is a promising approach to numerically reproduce ABL Boundary Layer development methods used in physical modeling.

The existence of the outer region “hairpins” and “hairpin packets” is visually assessed in a well-resolved DNS of a zero-pressure-gradient turbulent boundary layer at moderately high Reynolds number. For this purpose, 50 independent 2D streamwise–wall-normal slices at

$$Re_{\theta }=4300$$

R

e

θ

=

4300

are extracted. The slices are then used to mimic the coarser resolution PIV velocity fields of Adrian et al. J. Fluid Mech, 422:1–54, 2000 [

2

] using the mimicking procedure of Rahgozar et al. J. Turbul, 14(10):37–66, 2013 [

5

] based on Gaussian filtering and linear interpolation. Afterwards, in the same manner as Adrian et al. J. Fluid Mech, 422:1–54, 2000 [

2

], the mimicked fields are inspected in order to discover the signatures of hairpin and hairpin packets. The vortices that are identified as hairpins are then isolated and visualized in three dimensions using the fully resolved DNS data. In agreement with Adrian et al. J. Fluid Mech, 422:1–54, 2000 [

2

], signatures associated by them to hairpin and hairpin packets are observed frequently in the mimicked planes. However, the 3D character of the 2D signatures is found to be more convoluted than the proposed hairpin packet model.

Large-scale turbulent flow structures associated with positive and negative wall pressure fluctuations in a compressible turbulent boundary layer are investigated. Experiments are conducted in a closed-loop transonic wind tunnel at

$$\mathrm{Ma} = 0.5$$

Ma

=

0.5

–0.8, Re

$$_\tau = 5{,}100$$

τ

=

5

,

100

–9, 500 with combined velocity field and wall pressure measurements. Both, velocity and pressure statistics are analysed and compare well with existing low Mach number data. Spatial two-point correlation is applied to determine the size and orientation of the large-scale flow structures, which depending on the wall height have an averaged length scales of 4–6

$$\delta $$

δ

and a maximum inclination angel of

$${\approx }12^\circ $$

≈

12

∘

–

$$13^\circ $$

13

∘

. The wall pressure fluctuations are associated with shear layer structures and it is shown that positive pressure fluctuations are correlated with low speed large-scale flow structures over streamwise extents of 4–5

$$\delta $$

δ

.

Three-dimensional pressure–velocity correlations in a turbulent boundary layer have been investigated to understand the relationship between the pressure fluctuations and the coherent structures. Simultaneous measurements of the fluctuating pressure and velocity fields have been performed by the point pressure measurement technique and stereo PIV. The space–time three-dimensional structures of the pressure–velocity correlations,

$$R_{pu}$$

R

p

u

,

$$R_{pv}$$

R

p

v

and

$$R_{pw}$$

R

p

w

, are evaluated. The wall pressure fluctuations are closely coupled with large-scale coherent structures, i.e., large-scale sweep and ejection. For the pressure fluctuations in the field, the pressure–velocity correlations

$$R_{pu}$$

R

p

u

and

$$R_{pw}$$

R

p

w

exhibit a meaningful correlation in a region very extended in time in addition to the structures observed with the wall pressure. The Reynolds number effect is quantified from the data at

$$Re_\theta $$

R

e

θ

$$=$$

=

7 300, 10 000, and 18 000, it is mostly evidenced on the size and intensity of the correlations. Such 3D structures of the pressure–velocity correlations can be consistent with the evidence of large-scale and very-large-scale motions reported in the literature.

In this work, we revisit the coupling of the Algebraic Structure-Based Model with popular two-equation eddy viscosity models (EVM). We consider both the

$$v^{2}-f$$

v

2

-

f

model and variants of the

$$\kappa $$

κ

-

$$\omega $$

ω

model. Our aim is to explore the role of the EVM in these couplings. Computations of turbulent boundary layer over a flat plate and a fully developed channel flow are initially performed for validation purposes. Then, the case of a 2D steep, smooth hill is considered, for which additional LES computations were performed in order to ascertain the validity of the experimental data. The coupling of the ASBM with the

$$\kappa $$

κ

-

$$\omega $$

ω

-BSL model (hereafter called ASBM-BSL) showed superior robustness when compared to the ASBM-

$$v^{2}$$

v

2

-

f

hybrid model. Moreover, ASBM-BSL captures the size of the recirculation bubble more accurately, and overall yields a noticeable improvement in the prediction of the turbulent statistics in the recirculation region. All models fail to capture the correct shear stress profile at the top of the hill, exhibiting positive, non-realizable values near the wall. The present comparisons reveal a sensitivity of the hybrid closures to the choice of carrier model.

A new nested LES approach for computing high Reynolds number, wall-bounded turbulent flows is presented. The method is based on nested LES of the full-domain at coarse resolution, coupled with well-resolved LES of a minimal flow unit. The coupling between the two domains is achieved by renormalizing the kinetic energies of components of the mean velocity and the turbulent velocity fluctuations in both domains to that of the minimal flow unit in the near-wall region, and to that of the full-size domain in the outer region, at each time-step. The method can be implemented with a fixed number of grid points, independent of Reynolds number, in any given geometry, and is applicable to both equilibrium and nonequilibrium flows. The proposed method has been applied to LES of equilibrium turbulent channel flow at

$$1000\le Re_\tau \le 10{,}000$$

1000

≤

R

e

τ

≤

10

,

000

and LES of nonequilibrium, shear-driven, three-dimensional turbulent channel flow at

$$Re_\tau \simeq 2000$$

R

e

τ

≃

2000

. All computations were performed using a spectral patching collocation method, and employed resolutions of

$$64\times 64\times 17/33/17$$

64

×

64

×

17

/

33

/

17

in the full-size domain (

$$L_x \times L_y = 2\pi \times \pi $$

L

x

×

L

y

=

2

π

×

π

), and resolutions of

$$32 \times 64 \times 17/33/17$$

32

×

64

×

17

/

33

/

17

and

$$64 \times 64 \times 17/33/17$$

64

×

64

×

17

/

33

/

17

the minimal flow units (

$$l_x^+ \,\times \, l_y^+ \approx 3200 \times 1600 $$

l

x

+

×

l

y

+

≈

3200

×

1600

) of equilibrium and non-equilibrium channel flows, respectively. The dynamic Smagorinsky model with spectral cutoff filter was used as the SGS model in all the simulations. The results show that the proposed nested LES approach can predict the friction coefficient to within 5 % of Dean’s correlation in equilibrium turbulent channel flow, and the one-point turbulence statistics in good agreement with DNS and experimental data in turbulent channel flow and in shear-driven, three-dimensional turbulent boundary layer.

The paper is concerned with the issue of scaling of Reynolds stresses and the phenomenon of the outer peak of velocity fluctuations, which appears in adverse pressure gradient conditions. For this purpose, experimental data from favorable and adverse pressure gradient turbulent boundary layers, for Reynolds number varying from

$$Re_{\theta }\approx 2300\div 6200$$

R

e

θ

≈

2300

÷

6200

, have been analyzed. At pressure gradient conditions, the self-similarity cannot be obtained using the scale, which is constant across the boundary layer thickness. In this paper, we also propose a modification of the Alfredsson et al. (Eur J Mech B/Fluids 36, 167–175, 2012, [

1

]) expression, which is dedicated to ZPG flows. The new formulation, utilizing the shape factor

H

and pressure gradient parameter

$$\varLambda $$

Λ

, allows an extension of the validity of Alfredsson et al. proposal for pressure gradient flows.

Spatial and temporal statistics associated with spanwise aligned vortical structures are extracted from high repetition rate particle image velocimetry (HR-PIV) experimental measurements of a zero-pressure gradient turbulent boundary layer. Measurements were performed in the LTRAC water tunnel with a momentum thickness-based Reynolds number of

$$\text{ Re }_\theta = 2{,}250$$

Re

θ

=

2

,

250

. Streamwise wall-normal planes of the field were recorded at rate of

$$\varDelta t = 0.008\delta /U_\infty $$

Δ

t

=

0.008

δ

/

U

∞

, spanning a streamwise domain of

$$3.2\delta $$

3.2

δ

. This enables a single structure to be sampled approximately 400 times for a duration of 3.2

$$\delta /U_\infty $$

δ

/

U

∞

as it convects downstream. A model Oseen vortex is fit to each local peak in swirling strength, in order to detect and classify the radius, centroid velocity, circulation, and centroid location of each spanwise vortex. Attempts to track the evolution of these vortices show that on average these Oseen vortices only appear to remain temporally coherent for a time of 0.02

$$\delta /U_\infty $$

δ

/

U

∞

.

The downstream evolution of the vorticity field in the vicinity of hairpin-shaped regions of rotational motion appearing in the transitioning boundary layer is examined. It is shown that the dynamics of hairpins is inseparable from that of the nonrotational vorticity out of which they develop in a self-reinforcing process of ejection and reorientation. Widening the concept of structure to include the complete localized vorticity that produces hairpins, allows for a more complete and self-contained explanation of the boundary layer physics.

In the present work, direct numerical simulations of turbulent channel flow of a viscoelastic FENE-P fluid, at zero-shear friction Reynolds number equal to 180, are used to analyze the polymer extension mechanism. As a primary focus, the relative polymer stretch and the probability distribution function of the alignment between the conformation tensor and other relevant entities are investigated. In near-wall regions, polymers present a strong tendency to orient along the streamwise direction of the flow. Furthermore, the polymer extension seems to be strongly correlated to the alignment between both conformation tensor and the velocity fluctuations product tensor,

$$\mathbf { {\tau }^{\prime } }$$

τ

′

(defined as

$${{u^{\prime }}_i}{{u^{\prime }}_j}$$

u

′

i

u

′

j

). Joint probability density functions show that large positive polymer work fluctuations,

$${{E^{\prime }}_x}$$

E

′

x

, are closely related to the positive growth rate of the product of streamwise velocity fluctuations,

$${\partial _{t} {u^{\prime }}^2_x}$$

∂

t

u

′

x

2

. In contrast, small negative fluctuations of polymer work are observed in the regions of negative rate of

$${u^{\prime }}^2_x$$

u

′

x

2

. However, in both cases, polymers are predominantly oriented along the principal direction of

$$\mathbf { {\tau }^{\prime } }$$

τ

′

, which indicates the relevance of this tensor for the polymer-turbulence interaction mechanism.

We measure the velocity field in a horizontal field near the hot plate in turbulent convection using stereo PIV for

$${10^6<Ra_w<10^9}$$

10

6

<

R

a

w

<

10

9

and

$${5.2<Pr<4}$$

5.2

<

P

r

<

4

. We then extract the line plumes from this velocity field using a divergence criterion using the PIV technique on the obtained plume structures, which gives us the velocity field of the plume motion. The statistical analysis of this velocity field of the plume motion shows the coexistence of two different kinds of motion of the plumes, lateral merging and motion along the plumes.

The paper presents the results of numerical simulations of an incompressible flow in a converging–diverging channel performed with Large Eddy Simulation (LES) combined with the immersed boundary (IB) method. The computations are carried out using a high-order code with the spatial discretization based on the compact difference method for half-staggered meshes. IB method is implemented in the so-called direct forcing approach with a second-order interpolation near the boundaries. Two relatively new subgrid models are used in the simulations, i.e. the model proposed by Vreman, Phys Fluids 16:3670–3681, 2004, [

1

] and the model proposed by Nicoud et al., Phys Fluids 23:193–202, 2011, [

2

]. It is demonstrated that both of them perform well and there is no evident advantage for either of them. The mean and r.m.s velocity profiles agree with exemplary DNS data.

To the surprise of some of our colleagues, we recently recommended aspect ratios of at least 24 (instead of accepted values over last few decades ranging from 5 to 12) to minimize effects of sidewalls in turbulent duct flow experiments, in order to approximate the two-dimensional channel flow. Here we compile available results from hydraulics and civil engineering literature, where this was already documented in the 1980s. This is of great importance due to the large amount of computational studies (mainly Direct Numerical Simulations) for spanwise-periodic turbulent channel flows, and the extreme complexity of constructing a fully developed duct flow facility with aspect ratio of 24 for high Reynolds number with adequate probe resolution. Results from this nontraditional literature for the turbulence community are compared to our recent database of DNS of turbulent duct flows with aspect ratios ranging from 1 to 18 and

$$Re_{\tau ,c} \simeq 180$$

R

e

τ

,

c

≃

180

and 330, leading to very good agreement between their experimental and our computational results.

Large eddy simulations have been conducted to gain further insight into the drag-reducing mechanisms of riblets in zero-pressure gradient turbulent boundary layer. The retained groove geometry achieves 9.8 % drag reduction on the controlled zone developing from

$$Re_{\theta } = 670$$

R

e

θ

=

670

to 975. It is shown that the turbulent contribution to the drag—as defined by Fukagata et al. Phys. Fluids, 14(11):L73, 2002 [

7

]—is the most affected. In the light of the obtained results, energy and enstrophy budgets will finally conduct to isolate a key mechanism involved in the riblets drag reduction.

This paper deals with the extraction of turbulent structure correlated with the wall mass transfer in a curved swirling pipe flow behind an orifice. The cross-sectional velocity field behind the orifice is measured by the Stereo Particle Image Velocimetry (SPIV) and the results are analyzed by the proper orthogonal decomposition (POD). The instantaneous velocity field shows the asymmetric vortex structure in the cross section due to the combined effect of the swirling flow and the secondary flow generated at the upstream elbow. The POD analysis indicates that the highly turbulent flow is generated on the upper left-hand side of the pipe in the lower POD modes suggesting the occurrence of high wall-thinning rate due to the mass transfer enhancement, while that of the higher modes do not show such asymmetry. This result suggests that the lower POD modes of the velocity field contribute to the non-axisymmetric pipe-wall thinning behind an orifice in a curved swirling flow.

Turbulent flow in the annular gap between two concentric tubes of 38 and 95 mm diameter at Reynolds number of 79’000 is experimentally investigated. Measurements are conducted using planar particle image velocimetry (PIV) with spatial resolution of 23

$$\upmu $$

μ

m/pix and interrogation windows of 0.74

$$\times $$

×

0.74 mm

$$^{2}$$

2

. The experiments are aimed at scrutinizing the location of the extremums of the asymmetric profiles of velocity and turbulent statistics along with the relevant turbulent structures. The location of maximum average streamwise velocity

$$<$$

<

$$U$$

U

$$>_\mathrm{max}$$

>

max

and zero Reynolds shear stress

$$<$$

<

$$uv$$

u

v

$$>$$

>

are observed to be apart. Local minimum of

$$<$$

<

$$u^{2}$$

u

2

$$>$$

>

and

$$<$$

<

$$v^{2}$$

v

2

$$>$$

>

is also observed to coincide with

$$<$$

<

$$uv$$

u

v

$$>\, = 0$$

>

=

0

and different from

$$<$$

<

$$U$$

U

$$>_\mathrm{max}$$

>

max

. The experiments also demonstrate that the ejection events originating from the inner and outer walls play a dominant role in transport of turbulence toward the midsection of the annulus.

In this paper, we investigate the applicability of the predictive wall shear-stress model, recently developed by Mathis et al. J. Fluid Mech. 715, 163–180, 2013, [

17

], to environmental flows where near-wall information is typically inaccessible. This wall-model, which embeds the scale interaction mechanisms of superposition and modulation, is able to reconstruct the instantaneous wall (bed) shear-stress fluctuations in turbulent boundary layers. The database considered here comes from field measurements using acoustic Doppler velocimeters carried out in a shallow tidal channel (Suisun Slough in North San Francisco Bay). The model is first applied to a selected subset of data sharing common properties with the canonical turbulent boundary layer. Statistics and energy content of these predictions are found to be consistent with laboratory predictions and DNS results. The model is then used on the whole dataset, whose some of them having properties far from the canonical case. Even for these situations, the model is able to preserve the overall Reynolds trend. This study shows the great capability of the model for environmental applications, which is the only one able to predict both the correct energetic content and probability density function.

The paper is concerned with the experimental study of bursting process in turbulent boundary layer. For this purpose the novel identification process, developed by Dróżdż and Elsner, J Phys: Conf Ser 318(6):062007, 2011, [

3

] based on VITA technique combined with quadrant analysis was applied. By the detection of four possible combinations of instantaneous gradients of

u

and

v

phase-averaged velocity traces this method allows to demonstrate such properties of vortices motion as: swirling direction, ascending or descending direction, the trajectory inclination. The analysis gives an evidence of four types of vortical structures present in the TBL which are responsible for the production of Q-type events, namely prograde and retrograde vortices, with the ascending and descending direction of motion. It was found that detected coherent structures have dominant share of the overall energy of velocity fluctuations.

We present an experimental investigation and data analysis of a turbulent boundary layer flow at a significant adverse pressure gradient for two Reynolds numbers

$$Re_\theta =6200$$

R

e

θ

=

6200

and

$$Re_\theta =8000$$

R

e

θ

=

8000

. We perform detailed multi-resolution measurements by combining large-scale and long-range microscopic particle imaging. We investigate scaling laws for the mean velocity and for the total shear stress in the inner layer. In the inner part of the inner layer the mean velocity can be fitted by a log-law. In the outer part a modified log-law provides a good fit, which depends on the pressure gradient parameter and on a parameter for the mean inertial effects. Emphasis is on the Reynolds number effects on the mean velocity and shear stress.

The characteristics of three-dimensional intense

uv

-structures (Qs) in a strongly decelerated large-velocity-defect boundary layer are analyzed. The Q2 and Q4 structures are found to be different from those of turbulent channel flows studied by Lozano-Durán et al. (J Fluid Mech 694:100–130, 2012). They are less streamwise elongated, less present near the wall and wall-detached structures are more numerous. Moreover, contrary to channel flows, wall-detached Q2, and Q4 structures contribute significantly to the Reynolds shear stress.

LES results are presented for the flow over different bump profiles installed on the bottom wall of a channel. Three bump geometries are considered in order to investigate the effects of adverse pressure gradients and changes in curvature on the mean flow and Reynolds stresses. The first bump geometry corresponds to a profile for which DNS results are available at a Reynolds number

$$Re_{\tau } =$$

R

e

τ

=

617 based on the channel inlet friction velocity. The other two geometries are generated by modifying the rear portion of the initial profile to produce a longer APG region and promote smoother curvature changes as compared to the original profile. LES computations are performed at the same Reynolds numbers than previous DNS, which is also used to validate LES results in the original bump. Finally, RANS results are also presented for the three bump profiles. RANS computations are performed using a two-equation eddy-viscosity Shear Stress Transport (SST) model and one Reynolds stresses transport model.

Experimental results of turbulent separating boundary layer, subjected to nominally 2D pulsed excitation, are presented and discussed. The effect of the adverse pressure gradient on the vortices circulation and convection speed has been documented. A search for instability mechanism did not result in any that were amplified. Therefore, pulsed excitation that intermittently enhances the skin friction with optimal time lag should be explored.

This contribution reports on near-wall flow field measurements in turbulent Rayleigh-Bénard convection (RBC) in air at a fixed Prandtl number

$$\mathrm {Pr} = 0.7$$

Pr

=

0.7

and Rayleigh number

$$\mathrm {Ra} = 1.45 \times 10^{10}$$

Ra

=

1.45

×

10

10

. For the experiment, the large-scale convection (LSC) was confined to a rectangular box of

$$2.5 \times 2.5 \times 0.65\,\mathrm {m}^3$$

2.5

×

2.5

×

0.65

m

3

made of transparent acrylic sheets. Prior video-graphic visualizations of the bottom boundary layer flow by means of laser light sheet illumination of small particles indicated the presence of highly dynamic flow behaviour at flow conditions that classical stability analysis predicts to still be in the laminar regime. While theory predicts a transition to turbulence at Reynolds numbers

$$\mathrm {Re}_\delta \approx 420$$

Re

δ

≈

420

, the present investigation exhibits highly unsteady flow at a much lower Reynolds number of

$$\mathrm {Re}_\delta \approx 260$$

Re

δ

≈

260

based on boundary layer thickness. With the help of the PIV data, it can be demonstrated that the entrainment of turbulent structures from the mean wind into the boundary layer acts, alongside with the destabilization due to inner shear, as a second mechanism on its path to turbulence. Both contributions must be considered when predicting the critical bound towards the

ultimate regime

of thermal convection. The measurements rely on the acquisition of long, continuous sequences of particle image velocimetry (PIV) data from which both statistical and spectral information can be retrieved. Contrary to conventional implementation of the PIV technique the field of view is restricted to a narrow strip, generally extending in wall-normal direction. In this way, both the acquisition frequency and the total number images of the employed high-speed camera are proportionally increased. The temporally oversampled data allows the use of multi-frame PIV processing algorithms which reduce measurement uncertainties with respect to standard dual-frame analysis.

Large-scale streaky structures play an important role in the turbulence production process of a boundary layer. Adrian has proposed a model at very large scales which could explain the organization of the boundary layer, but at high Reynolds number, their main characteristics (size, intensity and life time) and the way they interact with the near-wall structures is still not fully understood. To tackle these points, an experimental database at a Reynolds number based on momentum thickness

$$Re_{\theta }$$

R

e

θ

close to 9800 was recorded in the Laboratoire de Mécanique de Lille wind tunnel with stereo-PIV (SPIV) and hot-wire anemometry (HWA). With a Linear Stochastic Estimation (LSE) procedure based on correlations computation, a three-component velocity field was reconstructed at high frequency from stereo-PIV at 4 Hz and hot-wire data at 30 kHz. To extract large streaky structures, a threshold is applied to normalized streamwise velocity fluctuations from the reconstructed PIV field, and then 3D morphological operations (erosion and dilatation) are combined with a volume-size-based cleaning procedure to remove the noise and smooth the object boundaries. Some statistical characteristics of the large streaks are obtained.

The fundamental study of the near-wall structure organization in turbulent flows is crucial to understand the self-generation process of turbulence. To investigate such phenomena, an experiment of high-repetition, 6-camera tomo-PIV in a boundary layer was performed. Vector fields generated from BIMART high-quality reconstructed volumes resulted in low measurement uncertainties. The comparison of turbulence statistics from tomographic PIV and hot-wire anemometer data shows an excellent agreement. Preliminary vortex detection from Q-criterion is presented and allows the identification of dispersed vortices around the low-speed streaks in the boundary layer. Nevertheless an accurate identification of turbulent structures is not yet achieved. The postprocessing is being reviewed and the discussion of the interaction and evolution of turbulent structures will be addressed in a future paper.

Direct numerical simulation of a turbulent boundary layer developing over a superhydrophobic surface (SHS) was performed in order to investigate the effects of SHS on skin friction drag. Significant modifications of near-wall turbulence structures were observed, which resulted in large skin friction drag reduction. For the considered Reynolds number ranges and SHS geometries, it was found that the effective slip length normalized by viscous wall units was a key parameter. It was shown that the effective slip length should be on the order of the buffer layer in order to have the maximum benefit of drag reduction. It was also found that the width of SHS, relative to the spanwise width of near-wall turbulence structures, was also a key parameter to the total amount of drag reduction. Similarities and differences between the present turbulent boundary layer over SHS and our earlier work of turbulent channel flows with SHS are also discussed.

The structure and dynamics of turbulence in turbulent channel flow with super-hydrophobic (SH) walls has been investigated using DNS with Lattice Boltzmann methods. The channel walls consisted of longitudinal arrays of SH microgrooves of width

g

, separated by distances of

w

. The liquid/gas interfaces in the SH walls were modeled as idealized, flat, shear-free surfaces. Simulations were performed at a bulk Reynolds number of

$$Re_b = U_{bulk} h/\nu = 3600$$

R

e

b

=

U

b

u

l

k

h

/

ν

=

3600

, corresponding to

$$Re_{\tau _0} = u_{\tau _0} h / \nu \approx 223$$

R

e

τ

0

=

u

τ

0

h

/

ν

≈

223

. Drag reductions (DR) of 5–47 % and 51–83 % were obtained with

$$g/w=1$$

g

/

w

=

1

, and

$$g/w = 7$$

g

/

w

=

7

and

$$g/w = 15$$

g

/

w

=

15

, respectively. DR was found to be primarily due to surface slip. Mathematical analysis shows that the magnitude of DR in both laminar and turbulent flow is given by

$$DR = U_{slip}/U_{bulk} + O(\varepsilon )$$

D

R

=

U

s

l

i

p

/

U

b

u

l

k

+

O

(

ε

)

. In laminar flow, where DR is purely due to surface slip,

$$\varepsilon $$

ε

is zero. In turbulent flow,

$$\varepsilon $$

ε

attains a small nonzero value at high DR, reflecting additional DR effects resulting from modification of the turbulence dynamics in the interior of the flow due to the presence of the SH surface. Analysis of the turbulence statistics and kinetic energy budgets in the drag-reduced flow reveals that the influence of the SH surface remains confined to a surface layer of thickness on the order of the SH microgrooves width,

g

. Outside of this layer, the ‘normalized’ turbulence dynamics proceeds as in regular turbulent channel flow. Within the surface layer, the presence of the pattern of longitudinal microgrooves on the SH surfaces gives rise to spanwise variations in all Reynolds-averaged turbulence quantities, leading to development of a mean secondary flow and additional turbulence production and Reynolds shear stresses within the surface layer of the SH channel.

A method inspired by del Álamo and Jiménez, J Fluid Mech 640:5–26, 2009, [

7

] is derived to assess the wavelength-dependent convection velocity in a zero pressure gradient spatially developing flat plate turbulent boundary layer at

$$Re_\theta = 13\,000$$

R

e

θ

=

13

000

for all wavelengths and all wall distances, using only estimates of the time power spectral density of the streamwise velocity and of its local spatial derivative. The resulting global convection velocity has a least-squares interpretation and is easily related to the wavelength-dependent convection velocity. The method intrinsically provides an estimation of the validity of Taylor’s hypothesis by a correlation coefficient identical to the one from del Álamo and Jiménez, J Fluid Mech 640:5–26, 2009, [

7

]. The results reveal some similarities between the convection of the superstructures, the hairpin packets, and the near-wall structures. The convection velocity of the superstructures is isolated by restricting the global convection velocity to the largest wavelengths. The spatial spectrum is estimated from the temporal spectrum using the frequency-dependent convection velocity. The results are consistent with a classical correlation-based evaluation.

A Numerical experiment that isolates the motions at a given spanwise length scale is performed based on previous observation on the self-sustaining nature of the eddies in the logarithmic and the wake outer regions [

7

,

8

]. It is shown that the statistics of the isolated self-sustaining motions at a given spanwise length scale are strikingly similar to those of the single attached eddy postulated by Townsend and Perry [

1

,

2

,

5

,

6

], demonstrating the existence of the attached eddies in turbulent channel flow. Inspecting one-dimensional spectra also leads to build a complete form of the self-similarity of the streamwise length scale and the wall-normal location of all the coherent structures known, including near-wall streaks, quasi-streamwise vortices, very-large-scale motions, and large-scale motions.

The internal boundary layer (IBL) is an important phenomenon in atmospheric flows which is associated with a step change in the surface roughness. This phenomenon also relates to industrial flows, where a wall may exhibit abrupt changes in surface roughness, perhaps related to corrosion. The present study reports new wind tunnel measurements which consider a Smooth–Rough–Smooth (SRS) configuration. The rough surfaces were created using 40-grit sandpaper glued onto the ground plane of a wind tunnel, and mean velocity measurements were collected using a boundary layer Pitot tube. The development of the IBL is clearly evident in the streamwise evolution of the mean velocity profiles. The results indicate that once the flow encounters the step change in roughness, the flow immediately next to the wall is decelerated due to the enhanced skin friction associated with the surface roughness. The roughness effects propagate further into flow as the IBL grows in the streamwise direction. However, when the surface condition changes back to smooth, the flow begins to accelerate, but does not recover to the initially smooth profile. This implies that some regions of the velocity profile preserve a “memory” of the previous surface condition, and therefore are not in equilibrium with the local surface.

Understanding the turbulence organization near a wall is necessary to help improving turbulence models. From the experimental point of view, many researchers have worked on this subject since the fifties. Recently, Foucaut et al. (Exp. Fluids 50(4, Sp. Iss. SI):839–846, 2011) [

16

] have proposed a new idea to compute the 3D correlation tensor from two normal velocity fields when there are two homogeneous directions in the flow. The idea of the present contribution is to propose a specific SPIV experiment which allows the computation of the full 3D spatial correlation tensor in the near wall region of the TBL. This experiment composed of two Stereoscopic PIV planes normal to the wall which were simultaneously recorded was performed in the LML wind tunnel. The 3D correlation is then computed from the two velocity planes in order to give some information about the near wall turbulence organization. Conditioning the average by specific events allows us to improve the analysis of the organisation. It can evidence the link between the events.

Turbulent flows present several compact and spatially coherent regions generically known as coherent structures. The understanding of these structures is closely related to the concept of vortex, whose definition is still a subject of controversy within the scientific community. In particular, the role of objectivity in the definition of vortex remains a largely open question. The three most usual criteria for vortex identification (

Q

,

$$\varDelta $$

Δ

and

$$\lambda _2$$

λ

2

) are non-objective since they all depend on the fluid’s rate-of-rotation, which is not invariant to the reference frame. In the present work, we propose an objective definition of these criteria by using the concept of relative rate-of-rotation with respect to the principal directions of the strain rate tensor. We also explore two novel naturally objective flow classification criteria. All the criteria are applied to instantaneous velocity fields obtained by DNS of both Newtonian and viscoelastic turbulent channel flows. The analysis is carried out here for four friction Reynolds numbers from 180 to 1000, emphasizing the difference between objective and non-objective and classification criteria, as well as between Newtonian and non-Newtonian flows. Moreover, we try to obtain from the results of flow classification criteria information related to the polymer drag reduction phenomenon.

An experiment was performed in the LML boundary layer facility to determine all of the derivative moments needed to estimate the dissipation. The Reynolds number was

$$Re_\theta = 7500$$

R

e

θ

=

7500

or

$$Re_\tau = 2300$$

R

e

τ

=

2300

. A detailed analysis of the errors in derivative measurements was carried out, as well as applying and using consistency checks derived from the continuity equation and a local homogeneity hypothesis. Local homogeneity estimates of the dissipation are accurate everywhere within a few percent. Both local axisymmetry and local isotropy work almost as well outside of

$$\mathrm{y}^+ = 100$$

y

+

=

100

, but only local axisymmetry provides a reasonable estimate close to the wall.